A plate theory for nematic liquid crystalline solids

• Published in: Journal of the mechanics and physics of solids Vol. 144; p. 104101
• Main Authors: Mihai, L. Angela, Goriely, Alain
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01.11.2020; Elsevier BV
• Subjects: Constitutive models; Crystal structure; Crystallinity; Deformation; Elastic deformation; Elastic plates; Equilibrium equations; Horses; Liquid crystals; Mathematical models; Multiplicative decomposition; Nematic crystals; Nematic solids; Nonlinear deformation; Plate theory; Residual stress; Stress; Stress distribution; Two dimensional models; Nonlinear deformation; Nematic solids; Elastic plates; Liquid crystals; Multiplicative decomposition; Stress
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2020.104101

We derive a Föppl-von Kármán-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we rely on the deformation decomposition of a nematic solid into an elastic deformation and a natural shape change. The full solution to the resulting equilibrium equations consists of both the deformation displacement and stress fields. The model equations are applicable to a wide range of thin nematic bodies subject to optothermal stimuli and mechanical loads. For illustration, we consider certain reversible natural shape changes in simple systems which are stress free, and their counterparts, where the natural deformations are blocked and internal stresses appear. More general problems can be addressed within the same framework.